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Properties

Label 294.4.m
Level $294$
Weight $4$
Character orbit 294.m
Rep. character $\chi_{294}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $336$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.m (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(294, [\chi])\).

Total New Old
Modular forms 2064 336 1728
Cusp forms 1968 336 1632
Eisenstein series 96 0 96

Trace form

\( 336 q + 6 q^{3} + 112 q^{4} - 16 q^{5} - 24 q^{6} - 28 q^{7} + 252 q^{9} + O(q^{10}) \) \( 336 q + 6 q^{3} + 112 q^{4} - 16 q^{5} - 24 q^{6} - 28 q^{7} + 252 q^{9} + 52 q^{10} + 420 q^{11} + 24 q^{12} - 12 q^{13} + 32 q^{14} + 210 q^{15} + 448 q^{16} + 636 q^{17} - 482 q^{19} - 320 q^{20} + 36 q^{21} + 308 q^{22} - 28 q^{23} + 48 q^{24} + 882 q^{25} + 1216 q^{26} - 108 q^{27} + 104 q^{28} + 168 q^{29} - 156 q^{31} + 138 q^{33} - 304 q^{34} + 960 q^{35} - 2016 q^{36} - 1652 q^{37} - 3400 q^{38} - 2688 q^{39} - 464 q^{40} + 40 q^{41} + 84 q^{42} - 84 q^{43} + 1680 q^{44} + 1872 q^{45} + 392 q^{46} + 5392 q^{47} + 1152 q^{48} + 4156 q^{49} - 224 q^{50} + 4368 q^{51} + 1256 q^{52} + 2716 q^{53} + 108 q^{54} + 2186 q^{55} - 224 q^{56} + 252 q^{57} - 2856 q^{58} - 3220 q^{59} - 2184 q^{60} - 4942 q^{61} - 3968 q^{62} - 1368 q^{63} - 3584 q^{64} + 224 q^{65} + 528 q^{66} - 798 q^{67} - 1040 q^{68} - 1896 q^{69} + 1760 q^{70} + 112 q^{71} - 6122 q^{73} + 5264 q^{74} + 738 q^{75} - 400 q^{76} - 4900 q^{77} - 1680 q^{78} - 1456 q^{79} - 256 q^{80} + 2268 q^{81} - 768 q^{82} - 14272 q^{83} - 648 q^{84} - 1344 q^{85} + 784 q^{86} + 2856 q^{87} + 2128 q^{88} - 1424 q^{89} - 936 q^{90} + 5830 q^{91} + 224 q^{92} - 1806 q^{93} - 24 q^{94} + 18872 q^{95} + 192 q^{96} + 14420 q^{97} + 240 q^{98} - 504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)